# Equations Involving Absolute Values

Solving Equations Involving Absolute Values

Solving equations involving absolute values is one of the most important topics in linear equations. In this hub I present several examples with their complete solution. Hope you will find this helpful. This hub presents five sample exercises which demonstrate solving linear equations involving absolute values.

Example one : 3 / X + 5/ = 12

1/3 ( 3 /X + 5/) = 12 (1/3)

/X + 5 / = 4

X + 5 = 4

X = 4 -5 = - 1

X + 5 = -4

X = -4 -5 = -9

Example two : /3X – 1/ + 10 = 25

/3X – 1/ = 25 -10

/ 3X – 1 / = 15

3X – 1 = 15

3X = 15 + 1 = 16

1/3 (3X) = 16 (1/3)

X = 16/3

3X – 1 = -15

3X = -15 + 1

1/3(3X) = -14(1/3)

X = -14/3

Example Three : /3X + 5/ = 5X + 2

3X + 5 = 5X + 2

3X - 5X = 2 - 5

(-1/2)-2X = -3(-1/2)

X = 3/2

3X + 5 = -(5X + 2)

3X + 5 = -5X -2

3X + 5X = -2 -5

(1/8) 8X = -7(1/8)

X = -7/8

Example Four : ½ /3X + 5/ = 6X + 4

2 (1/2 /3X + 5/ ) = (6X + 4 ) 2

/3X + 5 / = 12X + 8

3X + 5 = 12X + 8

3X - 12X = 8 – 5

-9X = 3

(-1/9) -9X = 3 (-1/9)

X = -1/3

3X + 5 = -(12X + 8)

3X + 5 = -12X -8

3X + 12X = -8 -5

(1/15)15X = -13(1/15)

X = -13/15

Example five : 7 /8 – 3X/ = 21X -49

1/7(7 /8-3X/ ) = ( 21X - 49) 1/7

/8 – 3X / = 3X - 7

8 - 3X = 3X - 7

– 3X -3X = -7 -8

(-1/6)-6X = -15 (-1/6)

X = 15/16

8 -3X = -(3X -7)

8 – 3X = -3X + 7

-3X+3X = 7 – 8

0 = -1

No solution

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